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As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite number with an aliquot sum of 11, following 18. 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35).
[21] [20] In 1956, the conjecture was proven by John Selfridge. [ 22 ] [ 20 ] [ 2 ] In 1970, Solomon W. Golomb and John Selfridge showed that the unicursal polygonal path of 2 n − 2 segments exists on the n × n array for all n > 3 with the further constraint that the path be closed , i.e., it starts and ends at the same point. [ 20 ]
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
Dale and Dee Warner had been partners in life and business since they started their first company together in 2005—the year before they got married.
In mathematics, the n th Motzkin number is the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have diverse applications in geometry , combinatorics and number theory .
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These include Starfall, ABC mouse, [172] PBS Kids Video, Teach me, and Montessori crosswords. [173] Educational technology in the form of electronic books [109] offer preschool children the option to store and retrieve several books on one device, thus bringing together the traditional action of reading along with the use of educational technology.